1. Past studies have indicated that 85.6% of all enrolled college students in the U.S. are undergraduates. A random sample of 500 enrolled college students in a particular stats revealed that 420 of the students were undergraduates. Is there enough evidence to conclude that the percentage of undergraduates from this particular state differs from the national percentage?

a. (2points) What type of test would be appropriate for this situation? (one tailed test or two tailed test?)

b. (2points) State the null and the alternate hypotheses.

c. (2points) Perform the appropriate test and report the P-value

d. (2points) Use your P-value to make a conclusion about the problem. Are you accepting or rejecting the null hypothesis?

e. (2 Points).Find a 95% confidence interval forpercentage of undergraduates from this particular state differs from the national percentage

2.The State Superintendent of Schools consistently states that the average salary of all substitute teachers in every school district is at least $60 per day. The president of the teachers' union believes that the average salary is less than $60 per day. So, she sample eight school districts to help test her claim.

The daily salaries she found for the districts were $60 $56 $60 $55 $70 $55 $60 and, $55

a. (2points) What statistical test should be performed? Should this test be one sided or two?

b. (2points) Which condition has to be satisfied for the test that we did not have to check for the test on proportions?

c. (2point) Write the two hypotheses for the problem.

d. (1point) Make a sketch of the distribution indicatingthe test statistic and p.

e. (2points) Compute the appropriate statistical test and report the test statistics and associated p-value.

f. (1point) In the context of the problem, write a conclusion to the study and substantiate your conclusion using statistical arguments. Use an alpha level of 0.05.

g. (2points) Find a 95% confidence interval for the true daily salary based on the data.